Towards finding hay in a haystack: explicit tensors of border rank greater than 2.02m in C^m⊗ C^m⊗ C^m

12/26/2019

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by   J. M. Landsberg, et al.

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We write down an explicit sequence of tensors in C^m⊗ C^m⊗ C^m, for all m sufficiently large, having border rank at least 2.02m, overcoming a longstanding barrier. We obtain our lower bounds via the border substitution method.